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Suppose in the milliseconds after the big bang the cosmic egg had aquired some large angular momentum. As it expanded, keeping the momentum constant (not external forces) the rate of rotation would have slowed down, but it would never reach zero.

What implications would that have to measurments to distant supernova and CMB radiation? Do we have any experimental data that definitely rules out such as scenario? And to what confidence level?

Edit A Recent Article suggests that the universe might indeed be spinning as a whole. Anyone care to poke holes at it?

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I'm interested to see the answers. However, my first thought is "rotating relative to what?" I'm not so sure it's meaningful to talk about the entire universe rotating. –  Tim Goodman Nov 18 '10 at 7:46
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What about Gödel's solution, Tim? It's true that one of the motivations for Einstein to construct GR was the Machian principle, but it turns out that GR allows geometries that violate the principle. –  Raskolnikov Nov 18 '10 at 7:51
    
@Raskolnikov: Good point with the Gödel metric –  Tim Goodman Nov 18 '10 at 10:04
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@Tim: While linear motion is relative, it is not true about angular motion. –  Piotr Migdal Nov 18 '10 at 10:13
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The discovery.com article links to the actual paper: arxiv.org/abs/1104.2815 If this is right, then I guess it would be the first possible hint of a nonzero rate of rotation for the universe. He doesn't attempt to state his results in terms of an angular velocity. I doubt that this type of anisotropy is consistent with inflation...? –  Ben Crowell Jul 26 '11 at 1:10
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If you believe wholeheartedly in Mach's principle, then there is no way to test empirically for rotation of the universe as a whole, since there is nothing else for it to be rotating relative to. However, general relativity is not very Machian, and it offers a variety of ways in which an observer inside a sealed laboratory can detect whether the lab is rotating. For example, she can observe the motion of a gyroscope, or measure whether the Sagnac effect is zero. There are alternative theories of gravity, such as Brans-Dicke gravity, that are more Machian than GR,[Brans 1961] and in these theories there is probably no meaningful sense in which the universe could rotate. However, solar-system tests[Bertotti 2003] rule out any significant deviations from GR of the type predicted by Brans-Dicke gravity, so that it appears that the universe really is as non-Machian as GR says it is.

It is therefore possible according to general relativity to have cosmologies in which the universe is rotating. Historically, one of the earliest cosmological solutions to the Einstein field equations to be discovered was the Gödel metric, which rotates and has closed timelike curves. If we lived in a rotating universe such Gödel's example, the rate of rotation would have to be expressed in terms of angular velocity, not angular momentum. Angular velocity is what is measured by a gyroscope or the Sagnac effect, and GR doesn't even have a definition of angular momentum that applies to cosmological spacetimes.

A rotating universe does not have to have a center of rotation, and it can be homogeneous. In other words, we could determine a direction in the sky and say that the universe was rotating counterclockwise at a certain rate about the line connecting us to that point on the celestial sphere. However, aliens living somewhere else in the universe could do the same thing. Their line would be parallel to ours, but there would be no way to tell whether one such line was the real center of rotation.

To find out whether the universe is rotating, in principle the most straightforward test is to watch the motion of a gyroscope relative to the distant galaxies. If it rotates at an angular velocity -ω relative to them, then the universe is rotating at angular velocity ω. In practice, we do not have mechanical gyroscopes with small enough random and systematic errors to put a very low limit on ω. However, we can use the entire solar system as a kind of gyroscope. Solar-system observations put a model-independent upper limit of 10^-7 radians/year on the rotation,[Clemence 1957] which is an order of magnitude too lax to rule out the Gödel metric.

A rotating universe must have a certain axis of rotation, so it must have a particular type of anisotropy that picks out a certain preferred direction. We can therefore look at the cosmic microwave background and see whether its anisotropy contains a preferred axis.[Collins 1973] Such observations impose a limit that is tighter than provided by solar-system measurements (perhaps 10^-9 rad/yr[Su 2009] or 10^-15 rad/yr[Barrow 1985]), but such limits are model-dependent.

Because all of the present observation are consistent with zero rotational velocity, it is not possible to attribute any prominent cosmological role to rotation. Centrifugal forces cannot contribute significantly to cosmological expansion, or to the way your head feels when you're hung over.

Brans and Dicke, "Mach's principle and a relativistic theory of gravitation," Phys. Rev. 124 (1961) 925, http://loyno.edu/~brans/ST-history/

Bertotti, Iess, and Tortora, "A test of general relativity using radio links with the Cassini spacecraft," Nature 425 (2003) 374

Clemence, "Astronomical time," Rev. Mod. Phys. Vol. 29 (1957) 2

Collins and Hawking, "The rotation and distortion of the universe," Mon. Not. R. Astr. Soc. 162 (1973) 307

Hawking, "On the rotation of the universe," Mon. Not. R. Astr. Soc. 142 (1969) 529

Barrow, Juszkiewicz, and Sonoda, "Universal rotation: how large can it be?," Mon. Not. R. Astr. Soc. 213 (1985) 917, http://adsabs.harvard.edu/full/1985MNRAS.213..917B

Su and Chu, "Is the universe rotating?," 2009, http://arxiv.org/abs/0902.4575

[This is a physicsforums FAQ entry that I wrote with input from users George Jones, jim mcnamara, marcus, PAllen, tiny-tim, and vela.]

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Hi Ben. "Their line would be parallel to ours, but there would be no way to tell whether one such line was the real center of rotation." interesting, so a given object between the line joining both 'axes' (ours and those of the aliens) how would it displace due to universal rotation? How does this global rotation manifests in close objects? I understand that cosmological expansion manifests as galaxies increasing their distance locally, but i'm not clear what local consequences does this rotation have –  lurscher Jun 7 '13 at 21:41
    
@lurscher: Every inertial observer would see himself as being at rest and the universe as rotating about an axes through him. I had observers A and B. If you add a third object C, it's still the same story. Each of the three says the other two rotate about the axis passing through him. "Locally..." I guess it depends on how local you mean by local. Expansion isn't locally detectable either, unless you have a very charitable definition of local. –  Ben Crowell Jun 8 '13 at 1:09
    
Ben, i can in principle make a very long material thread, send it to another galaxy, and i should be able to extract work from the cosmological expansion. In a similar way, if a region has constant non-zero positive curvature, i should be able to create (again, in principle) a really big triangle with the same thread, but the inner angles of the triangle would sum above $\pi/2$ –  lurscher Jun 8 '13 at 1:33
    
I was hoping that the rotation would in principle mean that one of those threads, if put far way, would wind around another thread in a given direction, but it seems is not as simple as that –  lurscher Jun 8 '13 at 1:34
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I think in that case the universe will be homogeneous but not isotropic. Such geometries were classified by Bianchi, and they have parameters that are constrained be experiment (not my area of expertise, so I am not sure to what degree). As far as I know, there is no indication that angular momentum is needed to explain any cosmological observation.

Incidentally, I don't think general relativity (or any other current theory) obeys Mach's principal, as usually phrased it requires highly non-local effects. Frame dragging may be in the spirit of Mach's principle, but it follows from perfectly local interactions as encoded in GR.

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I am not sure about the Lense-Thirring effect in this case, but it is definitely true that a global rotation would be described by one of the Bianchi homogeneous but anisotropic (not isotropic) models as mentioned by Moshe. For beautiful pictures as to how the Cosmic Microwave Background anisotropy sky would look in those models, see the paper by Andrew Pontzen for example (Pontzen 2009).

Using the current CMB data, especially from the WMAP experiment, one can impose upper bounds on (and perhaps some day, detections of) those Bianchi models. This work goes at least as far back as Ted Bunn and collaborators' paper (Bunn, Fereira & Silk 1996)

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Thanks for mentioning my old paper! There are, not surprisingly, a bunch of better limits since our time. The constraints on the rotation of the Universe are very strict. –  Ted Bunn Jan 15 '11 at 18:41
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Mach's principle says that inertia arises from the mass of everything else in the universe, and so if the universe were rotating, it would be dragging us around in a circle with it, and because of that we wouldn't notice it. This frame-dragging actually happens, and is called the Lense-Thirring effect. If you were inside a massive rotating sphere, your frame of reference would be rotating with respect the rest of the universe outside the massive rotating sphere. However, I'm not sure whether the Lense-Thirring effect actually implies Mach's principle. Maybe somebody who knows more could help.

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Actually the sphere example is not a very good representation of space because of the vast distance. In a casual sphere you can say that the outer shell simply has more linear velocity than the inner shells, but when universe is in question, after a point you'd need velocities faster than light just to keep up with the angular speed w.r.t to the rotation axis. –  Cem Nov 18 '10 at 15:26
    
It's not clear this kind of argument works with general relativity. If you look at Kerr black holes, some of the space inside of a rotating black hole is rotating so fast because of frame dragging that an object cannot stand still with respect to the space outside the black hole. –  Peter Shor Nov 18 '10 at 19:12
    
The classic paper on the kind of thing you're talking about is C. Brans and R. H. Dicke, Physical Review 124 (1961) 925, loyno.edu/~brans/ST-history It's very readable. –  Ben Crowell Jul 26 '11 at 0:57
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If you say that universe is rotating "as a whole" you'd have to define a rotation axis. A rotation axis would cause some problems, like violating a homogeneous and isotropic universe, as proposed by cosmic inflation model.

By the way, you can not say that the universe is rotating at the same angular speed everywhere with respect to the rotation axis. This would cause faster than light linear velocities, although I simply used classical mechanics to calculate, maybe a relativistic model is possible.

The existence of such an angular momentum might have some implications though. For example, one could say, if the theory "Big Bounce"(http://en.wikipedia.org/wiki/Big_bounce) is correct, one could say the origin of the entire universe is a black hole with an angular momentum, that is, a rotating black hole with possibly no electrical charge.

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Yes a rotation axis, and this non-homogenous universe would be the implication (albeit, just slightly), but what evidence we would see to support or to shoot down this? It violates the inflation theory is not sufficient, because inflation is just a construct to explain the flatness of the universe, without much of a physical mechanism behind it (I may be wrong here). –  ja72 Nov 19 '10 at 5:26
    
If the universe is rotating, in a classical sense, without a rotation axis, and it is somehow possible, via relativity, to be rotating with the same angular velocity everywhere, my answer would be: It does not matter. Because then, It would be stationary for every single observer in this universe. Then we can ask the question "Rotating with respect to who?" which would be a pretty damn speculative question in my opinion. However back to your initial question: If the rotation is in the classical sense, there is no way to understand from inside the universe. –  Cem Nov 19 '10 at 11:10
    
You're reasoning based on your Newtonian intuition about rotation, and it's leading you to say things that aren't true in GR. You can have rotation with homogeneity. See, e.g., Barrow, J. D., Juszkiewicz, R., & Sonoda, D. H., "Universal rotation: how large can it be?," 1985 -- adsabs.harvard.edu/full/1985MNRAS.213..917B No, such a model does not lead to faster-than-c velocities. Worrying about >c velocities in this context doesn't make sense, because GR doesn't have a uniquely well-defined notion of the relative velocity of distant objects. –  Ben Crowell Jul 26 '11 at 0:54
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protected by Qmechanic Jun 7 '13 at 22:32

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